A Genetic Algorithm Based Approach for Solving Optimal Power Flow Problem

International Conference on Electronics, Computer and Communication (ICECC 2008)
University of Rajshahi, Bangladesh
ISBN 984-300-002131-3
A Genetic Algorithm Based Approach for Solving Optimal Power Flow Problem
A. B. M. Nasiruzzaman1
, M. G. Rabbani2
, M. R. I. Sheikh3
, M. S. Anower4
, Shubhashis K. Shil5
, Md. Ashraful
Haque6
1-2,4
EEE & 5-6
CSE Department, Rajshahi University of Engineering & Technology, 6204, Bangladesh
3
Kitami Institute of Technology, 165 Koen-cho, Kitami, Hokkaido, 090-8507, Japan
E-mail: nasir_zaman_eee@yahoo.com1
Abstract: The objective of this paper is to evolve
simple and effective methods for the optimal power
flow (OPF) problem in thermal units, which are
capable of obtaining optimal power generations for
a large-scale system. In optimization, GA has some
well-known advantages and disadvantages. The
classical (derivative based) method is applied as
economic dispatch problem with transmission
capacity constraints in literature. In this study, a
similar investigation for economic dispatch is
considered using simple Genetic Algorithm. The
performance of results obtained with both of the
methods is nearly same but from the viewpoint of
calculation time GA is much superior and its
effectiveness increases as the constraints of the
problem are increased.
Key Words: Genetic Algorithm, Optimal Power
Flow.
1. INTRODUCTION
In a practical power system, the power plants are not
located at the same distance from the centre of loads
and their fuel costs are different. Also under normal
operating conditions, the generation capacity is more
than the total load demand and the losses. Thus, there
are many options for scheduling generation. In an
interconnected power system the objective is to find
power scheduling of each power plant in such a way
as to minimize the operating cost. This means that
the generator’s power is allowed to vary within
certain limits so as to meet a particular load demand
with minimum fuel cost. This is called the optimal
power flow problem. The OPF is used to optimize
the power flow solution of large scale power system.
This is done by minimizing selected objective
function while maintaining an acceptable system
performance in terms of generator capability limits
and the output of compensating devices. The
objective functions, also, known as cost functions,
may represent economic costs, system security, or
other objectives.
The OPF has been studied by many researchers and
methods have been presented in several classical
papers [2], [3], and [4], and in well established
textbooks [5], and [6]. These classical methods
require specific assumptions on the objective
function such as continuity, differentiability.
Moreover, these methods are slowly convergent.
Genetic Algorithms (GA) are general search
technique based on the mechanism of natural
selection and natural genetics. In GA, genetic strings
represent search points. The search process uses
probabilistic transition rules instead of deterministic
ones as in traditional optimization method. The
search is conducted over a population of solutions.
Moreover, no specific assumptions on the objective
function, such as continuity, differentiability, etc. are
required in GA.
Genetic Algorithm is different from traditional or
conventional methods in four ways:
1. GA work with a coding of the parameter
set, not the parameters themselves.
2. GA search from a population of points, not
a single point.
3. GA use payoff (objective function)
information, not derivatives or other auxiliary
knowledge.
4. GA use probabilistic transition rules, not
deterministic rules.
In several papers [1] the optimal power flow problem
is solved using GA considering a power plant
composed of six generators.
In our paper, analysis is done for any number of
buses with any number of generators.
The OPF problem has a nonlinear objective function
having many variables and constraints. In this paper
GA has been used to solve the OPF problem as it
completely replaces classical mathematical
programming methods and also it is easy to
implement as an optimization procedure.
In view of the above, the main thrust of the research
work presented in this paper is to propose a new but
effective method for solving OPF using GA. The
main objectives of the research work presented are as
follows:
1. To present a systematic approach for the design
of a new method for solving optimal power flow
problem using GA.
2. To compare the performance of the GA based
method with the conventionally derivative based
methods [1], [2], [4], and [5].
476

ISBN 984-300-002131-3
2. MATHEMATICAL MODEL
Mathematical models are of fundamental importance
in understanding any physical system. This section
focuses on the modeling of OPF problem and its
formulation. The factors influencing power
generation at minimum cost are operating
efficiencies of generators, fuel cost, and transmission
losses. The most efficient generator in the system
does not guarantee minimum cost as it may be
located in an area where fuel cost is high. Also if the
plant is located far from the load center, transmission
losses may be considerably higher and hence the
plant may be overly uneconomical. Hence the
problem is to determine the generation of different
plants such that the total operating cost is minimum.
In all practical cases, the fuel cost of generator i with
power output iP can be represented as a quadratic
function of real power generation
2
iiiiii PPC γβα ++=
where, ,, ii βα and iγ represent unit cost
coefficients.
The economic dispatch problem is to find the real
power generation for each plant such that the
objective function (i.e., total production cost) as
defined by the equation
∑=
++=
n
i
iiiiit PPC
1
2
γβα
is minimum subject to the inequality constraints
given by
(max)(min) iii PPP ≤≤ gni ,......,2,1=
where (min)iP and (max)iP are the minimum and
maximum generating limits respectively for plant i,
subject to the constraint that generation should equal
total demand plus losses, i.e.,
∑=
+=
gn
i
LDi PPP
1
where tC is the total production cost, iC is the
production cost of the i-th plant, iP is the generation
of i-th plant, DP is the total load demand, and gn is
the total number of displaceable generating plants
and PL is the total transmission loss as a quadratic
function of the generator power outputs given by
Kron’s loss formula
∑∑∑ == =
++=
gg g n
i
ii
n
i
n
j
jijiL BPBPBPP
1
000
1 1
The coefficients ijB are called loss coefficients.
3. GENETIC ALGORITHM
Genetic algorithms are computerized search and
optimization algorithms based on the mechanics of
natural genetics and natural selection. They combine
the survival of the fittest among string structures with
a structured yet randomized information exchange to
form search algorithm with some of the innovative
flair of human search. In every generation, a new set
of artificial creatures (strings) is created using bits
and pieces of the fittest of the old; an occasional new
part is tried for good measure. While randomized,
genetic algorithms are no simple random walk. They
efficiently exploit historical information to speculate
on new search points with expected improved
performance [7], and [8].
3.1 General Structure of GA
The sequential steps for searching optimal solution
of PSS parameters using GA is shown in Fig.1.
Fig. 1 Computational flow chart.
3.2 Design Methodology
The design problem can be formulated as the
following optimization problem:
1. Minimize the objective function
2
iiiiii PPC γβα ++= subjected to
constraint maxmin PPP i ≤≤ . Here the fitness
477

ISBN 984-300-002131-3
function )0(ii CCf −= is taken and it is to be
minimized.
2. An initial population of 256 individuals is
generated each of 8 bits with the following
equations. So, N=8.
(a) First the accuracy with following
parameters is chosen:
12 −
−
= N
LU
XX
Accuracy ;
where maxPX U
= and minPX L
= .
(b) Chromosome/Individual value
= Accuracy*Si where Si=0,1,2,…,255.
3. From this initial population of 256, 128
individuals are taken randomly for every
generation.
4. Roulette Wheel Method of reproduction is used.
5. Single cross-site of crossover is used with
crossover rate 0.5 and mutation rate 0.05.
6. As a terminating condition number of
generation is chosen to be 100.
4. COMPARATIVE STUDY OF GA BASED
SOLUTION WITH CONVENTIONAL
SOLUTION
To evaluate the effectiveness of the proposed GA
based OPF problem solution examples from [5] are
taken as reference, the performance of the GA is
examined under different conditions
1. Economic dispatch neglecting losses and
generator limits (Example 7.4).
2. Economic dispatch neglecting losses and including
3. Economic dispatch including losses and
Comparative results are given in the following
tables: (Table 1, Table 2, and Table 3)
Table 1: Comparison of classical and genetic based
optimal dispatch of generation problem neglecting
losses and generator limits.
Classical Genetic
P1(MW) 400.0000 398.4313
P2(MW) 250.0000 250.9803
P3(MW) 150.0000 150.5882
Cost ($/h) 6682.20 6682.51
Time(sec) 50.765 0.9677
optimal dispatch of generation problem neglecting
losses and including generator limits.
Classical Genetic
P1(MW) 450.0000 447.3529
P2(MW) 325.0000 325.0000
P3(MW) 200.0000 202.6470
Cost ($/h) 8236.25 8237.66
Time(sec) 105.765 1.0103
optimal dispatch of generation problem including
losses and generator limits.
Classical Genetic
P1(MW) 35.0907 31.1764
P2(MW) 64.1317 67.0588
P3(MW) 52.4767 50.0000
Cost ($/h) 1592.65 1566.45
Time(sec) 250.765 1.723
From the tables it is evident that GA based solutions
are faster than the traditional derivative based
methods and the computational time differences are
much more prominent as the constraints are
increased.
5. CONCLUSION
A new approach for solving the challenging optimal
load flow problem is presented. The model for
solving the mentioned problem is formulated and
solved at various conditions. The results are
compared with the results obtained using traditional
methods. The results are quite similar except that GA
is much faster than the traditional ones. This
indicates that the GA approach is quite promising
and deserves serious attention because of its
probabilistic transition rules, not deterministic ones.
References
[1] A. Demirören and H.L. Zeynelgil, “The
Investigation of Environmental/Economic
Dispatch using a Genetic Algorithm”, proc. of
Modelling, Identification, and Control, MIC-
2003.
[2] R.C. Burchett, H. H. Happ, and D. R.
Vierath, “Quadratically Convergent Optimal
Power Flow,” IEEE Transactions PAS-103, no.
10, pp. 3267–3275, Nov. 1984.
[3] R.C. Burchett, H. H. Happ, and K. A.
Wirgao, “Large Scale Optimal Power Flow”
IEEE Transactions PAS-103, no. 10 pp. 3722–
3731, Oct. 1982.
478

ISBN 984-300-002131-3
[4] J. F. Dopaz, O. A. Klitin, G. W. Stagg, and
M. Watson “An optimization technique for real
and reactive power allocation” proc. of IEEE,
Vol. 55, no. 11, pp1877-1885, 1967.
[5] W. D. Stevenson, Jr, “Elements of Power
System Analysis”, McGraw-Hill Book
Company, 2002.
[6] Hadi Saadat, “Power System Analysis”, Tata
McGraw-Hill Publishing Company Limited,
2002.
[7] David E. Goldberg, “Genetic Algorithms in
Search, Optimization and Machine Learning”,
Pearson Education, 2002.
[8] S.Rajasekharan, S. A. Vijayalekshmi Pai,
“Neural Networks, Fuzzy Logic & Genetic
Algorithms”, Prentice Hall of India, 2003.
479

A Genetic Algorithm Based Approach for Solving Optimal Power Flow Problem

Recommended

More Related Content

What's hot (20)

Viewers also liked (16)

Similar to A Genetic Algorithm Based Approach for Solving Optimal Power Flow Problem (20)

More from Shubhashis Shil (11)

A Genetic Algorithm Based Approach for Solving Optimal Power Flow Problem